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A052217 Numbers whose sum of digits is 3. 41
3, 12, 21, 30, 102, 111, 120, 201, 210, 300, 1002, 1011, 1020, 1101, 1110, 1200, 2001, 2010, 2100, 3000, 10002, 10011, 10020, 10101, 10110, 10200, 11001, 11010, 11100, 12000, 20001, 20010, 20100, 21000, 30000, 100002, 100011, 100020, 100101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Joshua S.M. Weiner, Oct 19 2012: (Start)

It is a representation of the "energy states" of "multiplex" notation of 3 quantum of objects in a juggling pattern.

0 = an empty sit, or empty hand. 1 = one object resides in the site. 2 = two objects reside in the site. 3 = three objects reside in the site. (see A038447). (End)

A007953(a(n)) = 3; number of repdigits = #{3,111} = A242627(3) = 2. - Reinhard Zumkeller, Jul 17 2014

Can be seen as a table whose n-th row holds the n-digit terms {10^(n-1) + 10^m + 10^k, 0 <= k <= m < n}, n >= 1. Row lengths are then (1, 3, 6, 10, ...) = n(n+1)/2 = A000217(n). The first and the n last terms of row n are 10^(n-1) + 2 resp. 2*10^(n-1) + 10^k, 0 <= k < n. - M. F. Hasler, Feb 19 2020

LINKS

Vincenzo Librandi, T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 84 terms from Vincenzo Librandi, terms up to n=1140 from T. D. Noe)

FORMULA

T(n,k) = 10^(n-1) + 10^A003056(k) + 10^A002262(k) when read as a table with row lengths n(n+1)/2, n >= 1, 0 <= k < n(n+1)/2. - M. F. Hasler, Feb 19 2020

MATHEMATICA

Union[FromDigits/@Select[Flatten[Table[Tuples[Range[0, 3], n], {n, 6}], 1], Total[#]==3&]] (* Harvey P. Dale, Oct 20 2012 *)

Select[Range[10^6], Total[IntegerDigits[#]] == 3 &] (* Vincenzo Librandi, Mar 07 2013 *)

Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 18]], {s, IntegerPartitions[3]}]]] (* T. D. Noe, Mar 08 2013 *)

PROG

(MAGMA) [n: n in [1..100101] | &+Intseq(n) eq 3 ]; // Vincenzo Librandi, Mar 07 2013

(Haskell)

a052217 n = a052217_list !! (n-1)

a052217_list = filter ((== 3) . a007953) [0..]

-- Reinhard Zumkeller, Jul 17 2014

(PARI) isok(n) = sumdigits(n) == 3; \\ Michel Marcus, Dec 28 2015

(PARI) apply( {A052217_row(n, s, t=-1)=vector(n*(n+1)\2, k, t++>s&&t=!s++; 10^(n-1)+10^s+10^t)}, [1..5]) \\ M. F. Hasler, Feb 19 2020

CROSSREFS

Cf. A069521 to A069530, A069532 - A069537.

Cf. A007953, A218043 (subsequence).

Row n=3 of A245062.

Cf. A011557 (1), A052216 (2), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Cf. A242614, A242627.

Sequence in context: A017197 A051369 A069538 * A119507 A044436 A210282

Adjacent sequences:  A052214 A052215 A052216 * A052218 A052219 A052220

KEYWORD

base,easy,nonn

AUTHOR

Henry Bottomley, Feb 01 2000

EXTENSIONS

Changed offset from 0 to 1 by Vincenzo Librandi, Mar 07 2013

STATUS

approved

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Last modified August 4 01:48 EDT 2020. Contains 336201 sequences. (Running on oeis4.)